Social media users have lambasted US President Donald Trump over his reaction to deadly violence in the US city of Charlottesville as far-right activists took to the streets and clashed with counter-protesters.

After one person was killed and several injured in a car ramming that hit anti-racist demonstrators on Saturday, Trump said in a press conference: "We condemn in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides, on many sides."

Speaking from his private golf club in New Jersey, he said: "It has been going on for a long time in our country - not Donald Trump, not Barack Obama. It has been going on for a long, long time. It has no place in America."

nazis literally murder someone in broad daylight and people are still talking about "both sides."

Organised by far-right public figure Jason Kessler, a former journalist, Saturday's "Unite the Right" rally in Charlottesville, Virginia, was slated as one of the largest white supremacist rallies in the country's recent history.

Unite the Right was the third rally of its kind in Charlottesville throughout the last four months.

Far-right groups supported Trump's campaign and celebrated his electoral victory last November, seeing common cause in his efforts to limit immigration and repeal affirmative action, among other policies.

David Duke, the former leader of the Ku Klux Klan, a white supremacist organisation, praised Trump while speaking to reporters at Saturday's rally.

"This represents a turning point for the people of this country," he said. "We are determined to take our country back. We're going to fulfill the promises of Donald Trump. That's what we believed in, that's why we voted for Donald Trump ... because he said he's going to take our country back. And that's what we've got to do."

White nationalist Richard Spencer told The Associated Press he doesn't take responsibility for the violence and accused police of endangering lives in how they handled the rally.

"The idea that I could be held responsible is absurd. It's like blaming the fire department for a fire," said Spencer.

He also said he found Trump's comments on the Charlottesville violence to be "rather vague and kind of lame".

Pointing to white supremacist groups' support for Trump, other social media users mocked Trump's statement.